Related papers: Geometric Interpretation of Layer Normalization an…

Accurately predicting 3D structures and dynamics of physical systems is crucial in scientific applications. Existing approaches that rely on geometric Graph Neural Networks (GNNs) effectively enforce $\mathrm{E}(3)$-equivariance, but they…

Understanding the latent space geometry of large language models (LLMs) is key to interpreting their behavior and improving alignment. Yet it remains unclear to what extent LLMs linearly organize representations related to semantic…

Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the…

Vision-language models (VLMs) achieve strong performance on spatial reasoning benchmarks, yet it remains unclear whether this reflects structured 3D understanding or reliance on statistical shortcuts in natural images. We introduce a…

Vision-and-Language Navigation (VLN) has long been constrained by the limited diversity and scalability of simulator-curated datasets, which fail to capture the complexity of real-world environments. To overcome this limitation, we…

This paper presents a novel implicit representation of solid models. With this representation, every solid model can be effectively presented by three layered depth-normal images (LDNIs) that are perpendicular to three orthogonal axes…

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training…

Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be…

Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on the final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that…

The purpose of this report is in examining the generalization performance of Support Vector Machines (SVM) as a tool for pattern recognition and object classification. The work is motivated by the growing popularity of the method that is…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…

Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a…

Training state-of-the-art, deep neural networks is computationally expensive. One way to reduce the training time is to normalize the activities of the neurons. A recently introduced technique called batch normalization uses the…

The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings…

Batch normalization (BatchNorm) is a popular layer normalization technique used when training deep neural networks. It has been shown to enhance the training speed and accuracy of deep learning models. However, the mechanics by which…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle…

A language model (LM) is a mapping from a linguistic context to an output token. However, much remains to be known about this mapping, including how its geometric properties relate to its function. We take a high-level geometric approach to…